Frank, you need to clean out the fuel tank, filter if it has one, and fuel line. The problem is in the float bowl so you don't really need a full kit, but you do need the correct needle and seat. Replacing the seat requires a special screw which is difficult to get. Of course many people do a full carburetor clean-out once they work on it at all, and for that you would need the full kit.
If you post a picture of your carburetor we can establish which type it is, and give you some help with the float bowl overhaul if you wish. If you have the most common type of 12.5 hp carburetor in use about 20 years ago, you can read about the process in this thread:
https://www.outdoorking-forum.com.au/forum/ubbthreads.php?ubb=showflat&Number=15306However there are other types of carburetor that have been fitted to 12.5 hp engines, so it would be best to post a picture of it.
